By modeling an eel as a single capacitor answer the followingquestions. Use the
ID: 1748120 • Letter: B
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By modeling an eel as a single capacitor answer the followingquestions. Use the discharge time of 1 ms, the totalcurrent of 1 A, and the total voltage of 1 V to calculatethe capacitance of that capacitor. Then, using the dischargetime as the time constant of an RC circuit, calculate theresistance that the capacitor was discharged through. Assuming that the capacitor was discharged through a cylinder ofseawater, find a diameter and length of that cylinder that givesthe resistance you found. Thank you sooo much!!!!Explanation / Answer
Hi dfewer. Here, we try to model an eel as a capacitor. We are given: A charateristic discharge time = 1 ms = 10-3 of asecond A current I = 1 ampere A voltage V = 1 volt What do we know about capacitors? They act as "reservoirs" ofcharge. A capacitor creates an imbalance in the distribution of charge. It"borrows" (substract) a charge q that was at a point of spaceto relocate (add) it to another point. Evidently, we must "force"them to do so, as charge repels other charges of the same sign (allthey want to do is spread evenly through the conductor). In a circuit, electric forces are conveniently expressed in termsof difference-of-potentials (voltages), V. Then, the idea is this: The amount q of charge that we can accumulate (we force themto do so) has to be a function of the difference-of-potential V, and ithappens that it is a proportional relation: q = (constant) V. We name that constant the capacitance (C). It is ameasure of the amount of charge we can gather per unit ofpotential: charge/potential ~ [coulombs/volts] = [C/V] A special name was given to this combination of SI units: 1 C/V = 1farad. So, to calculate a capacitance, we need a charge and a voltage. Thelatter is given. How are we to get the charge? Look again at what is given to us. We are given a time. Thatdoesn't help much. But we are also given a current. But what is a current? It is the amount ofCHARGE (going through a point) per unit of TIME... But, hey, we have a current I and a time !! I = q / t ==> q = It, q = CV ==> C = q/V =It/V = (1 ampere)(10-3 sec)/(1 volt) =10-3 farad Next, we are asked to get the resistance R that the capacitor wasdischarged through. It is known (proof below) that the characteristic time associatedwith a RC circuit is = RC Thus R = /C = (10-3 s)/(10-3 farad) =1 . So with the order of magnitudes given above, we find that theresistance has to be of the order of 1 ohm. Just as a human beeing his mainly made of water, an eel is mostprobably mainly made of sea water. That's why we are asked to model an eel as a cylinderfilled with sea water. Now, different materials resist differently to the passage ofelectricity. That property is given by the RESISTIVITY of the susbstance. I'm sure that if I google "sea water resistivity" or something likeit, I'll get it.... ....[GOOGLE].... ....Yikes. It's harder than I tought.... I cannot find it. I hope you already have that somewhere in a textbook. Let r be the resistivity of sea-water (not of pure water!). The link between resistivity and resistance is: R = rL / A where L is the length and A the cross sectional area of a "wire"made of the specific substance. Here our "wire" is our sea-water cylinder. The cross-sectional area of a cylinder is the area of a circle:(radius)2. Thus r/R = A/L = (radius)2/(length) ==> (r cm)/(1 ) = r centimeters = (3.14)(radius)^2/(length) Note that the resistivity has units cm. So everything works as long as length = (radius)2/(r cm) So, let' say that the eel is 1 inch wide. [1 inch ~ 2.5 cm] Then radius = half-diameter = 2.5/2 centimeters; you plug that number in our relation above, and you'll get theassociated length. That's how I would do it. I hope it helps you. Mike ---------------------------------------------------------------------------- For my textbook list of the "standard" or "classic" textbooks inphysics: http://hubpages.com/hub/textbooks-for-the-standard-physics-curriculum
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